Henry and Margo both began traveling around a circular track. Henry is riding his bike, and Margo is walking. It takes Henry 7 minutes to make it all the way around, and Margo takes 12 minutes. How much time will pass until they meet at the starting line?

The problem can be solved using the concept of the least common multiple (LCM). Henry and Margo will meet at the starting line when the least common multiple of their times to complete one lap is reached.

Henry takes 7 minutes to complete one lap, and Margo takes 12 minutes. So, we need to find the LCM of 7 and 12.

### Steps to solve:
1. **Find the prime factorizations:**
   - 7 is a prime number, so its prime factorization is \( 7 \).
   - 12 can be factored as \( 2^2 \times 3 \).

2. **Determine the LCM:**
   - The LCM is the product of the highest powers of all prime factors that appear in either number.
   - LCM of 7 and 12 = \( 2^2 \times 3 \times 7 = 84 \).

Thus, the least common multiple of 7 and 12 is 84.

### Conclusion:
It will take **84 minutes** for Henry and Margo to meet at the starting line.

Would you like a more detailed breakdown of any of these steps, or have other questions?

Here are 5 related questions you could explore:
1. How many times will Henry and Margo each complete the track in 84 minutes?
2. If Henry were faster and took 5 minutes per lap, how would the LCM change?
3. What is the general formula for finding the LCM of two numbers?
4. How often would Henry and Margo meet if they had different starting points on the track?
5. How can the concept of relative speed be used to solve similar problems?

**Tip:** The LCM helps solve many timing problems involving cycles or periodic events.

Learn how to find the least common multiple (LCM) to determine when two people, Henry and Margo, will meet on a circular track. This math problem involves using number theory and prime factorization. It is ideal for students in Grades 6-8.

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